1) About what year was it you heard the song from your grandfather?
2) Does the fact he was Irish bear on the song? That is, was it an Irish song?
3) What country are you in, and if it's not a problem, what part of that country?
4) Was it a 'children's song' or an 'adult song'?
5) Not that it's cogent to a search, but is there a special reason you want to find this song?

As Noreen said, even a phrase or two could be a great help.